Bilinear form, bilinear auto-Backlund transformation, breather and lump solutions for a (3+1)-dimensional generalised Yu-Toda-Sasa-Fukuyama equation in a two-layer liquid or a lattice

Two-layer fluids are seen in fluid mechanics, thermodynamics and medical sciences. Lattices are seen in solid-state physics. In a two-layer liquid or a lattice, a (3+1)-dimensional generalised Yu-Toda-Sasa-Fukuyama equation is hereby studied with symbolic computation. Via the Hirota method, bilinear form and bilinear auto-Backlund transformation under certain coefficient constraints are obtained. Breather solutions are worked out based on the Hirota method and extended homoclinic test approach. Considering that the periods of breather solutions tend to infinity, we derive the lump solutions under a limit procedure. We observe that the amplitudes of the breather and lump remain unchanged during the propagation. Furthermore, we graphically present the breathers and lumps under the influence of different coefficients in the equation.

Automated summary

The study investigates a generalized equation in two-layer fluids or lattices, obtaining bilinear form and auto-Backlund transformation through symbolic computation. Breather solutions and lump solutions are derived based on the Hirota method and an extended homoclinic test approach. The study shows that the amplitudes of breathers and lumps remain unchanged during propagation, with graphical representation under varying coefficients.